Skip to main content

P Systems with Activation and Blocking of Rules

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 10867)

Abstract

We introduce new possibilities to control the application of rules based on the preceding applications, which can be defined in a general way for (hierarchical) P systems and the main known derivation modes. Computational completeness can be obtained even with non-cooperative rules and using both activation and blocking of rules, especially for the set modes of derivation. When we allow the application of rules to influence the application of rules in previous derivation steps, applying a non-conservative semantics for what we consider to be a derivation step, we can even “go beyond Turing”.

Keywords

  • Derivation Step
  • Computational Completeness Results
  • Backwards Activation
  • Register Machine
  • Evolutionary Time Line

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The work is supported by National Natural Science Foundation of China (61320106005, 61033003, and 61772214) and the Innovation Scientists and Technicians Troop Construction Projects of Henan Province (154200510012).

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-319-92435-9_1
  • Chapter length: 15 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   54.99
Price excludes VAT (USA)
  • ISBN: 978-3-319-92435-9
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   69.99
Price excludes VAT (USA)

References

  1. Alhazov, A.: A note on P systems with activators. In: Păun, Gh., Riscos-Núñez, A., Romero-Jiménez, A., Sancho-Caparrini, F. (eds.) Second Brainstorming Week on Membrane Computing, Sevilla, Spain, 2–7 February 2004, pp. 16–19 (2004)

    Google Scholar 

  2. Alhazov, A., Freund, R., Ivanov, S.: P systems with randomized right-hand sides of rules. In: 15th Brainstorming Week on Membrane Computing, Sevilla, Spain, January 31–February 5 2017 (2017)

    Google Scholar 

  3. Alhazov, A., Freund, R., Ivanov, S.: Hierarchical P systems with randomized right-hand sides of rules. In: Gheorghe, M., Rozenberg, G., Salomaa, A., Zandron, C. (eds.) CMC 2017. LNCS, vol. 10725, pp. 15–39. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-73359-3_2

    CrossRef  Google Scholar 

  4. Alhazov, A., Freund, R., Ivanov, S.: Systems with activation and blocking of rules (2018)

    Google Scholar 

  5. Alhazov, A., Freund, R., Ivanov, S., Oswald, M.: Observations on P systems with states. In: Gheorghe, M., Petre, I., Pérez-Jiménez, M.J., Rozenberg, G., Salomaa, A. (eds.) Multidisciplinary Creativity. Hommage to Gheorghe Păun on His 65th Birthday, Spandugino (2015)

    Google Scholar 

  6. Alhazov, A., Freund, R., Verlan, S.: P systems working in maximal variants of the set derivation mode. In: Leporati, A., Rozenberg, G., Salomaa, A., Zandron, C. (eds.) CMC 2016. LNCS, vol. 10105, pp. 83–102. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-54072-6_6

    CrossRef  Google Scholar 

  7. Alhazov, A., Ivanov, S., Rogozhin, Yu.: Polymorphic P systems. In: Gheorghe, M., Hinze, T., Păun, Gh., Rozenberg, G., Salomaa, A. (eds.) CMC 2010. LNCS, vol. 6501, pp. 81–94. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-18123-8_9

    CrossRef  Google Scholar 

  8. Aman, B., Csuhaj-Varjú, E., Freund, R.: Red–Green P automata. In: Gheorghe, M., Rozenberg, G., Salomaa, A., Sosík, P., Zandron, C. (eds.) CMC 2014. LNCS, vol. 8961, pp. 139–157. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-14370-5_9

    CrossRef  Google Scholar 

  9. Arroyo, F., Baranda, A.V., Castellanos, J., Păun, Gh.: Membrane computing: the power of (rule) creation. J. Univ. Comput. Sci. 8, 369–381 (2002)

    Google Scholar 

  10. Budnik, P.: What Is and What Will Be. Mountain Math Software (2006)

    Google Scholar 

  11. Calude, C.S., Păun, Gh.: Bio-steps beyond turing. Biosystems 77(1–3), 175–194 (2004)

    CrossRef  Google Scholar 

  12. Cavaliere, M., Freund, R., Oswald, M., Sburlan, D.: Multiset random context grammars, checkers, and transducers. Theor. Comput. Sci. 372(2–3), 136–151 (2007)

    MathSciNet  CrossRef  Google Scholar 

  13. Cavaliere, M., Genova, D.: P systems with symport/antiport of rules. In: Păun, Gh., Riscos-Núñez, A., Romero-Jiménez, A., Sancho-Caparrini, F. (eds.) Second Brainstorming Week on Membrane Computing, Sevilla, Spain, 2–7 February 2004, pp. 102–116 (2004)

    Google Scholar 

  14. Cavaliere, M., Ionescu, M., Ishdorj, T.O.: Inhibiting/de-inhibiting rules in P systems. In: Pre-proceedings of the Fifth Workshop on Membrane Computing (WMC5), Milano, Italy, June 2004, pp. 174–183 (2004)

    Google Scholar 

  15. Dassow, J., Păun, Gh.: Regulated Rewriting in Formal Language Theory. Springer, Berlin (1989)

    CrossRef  Google Scholar 

  16. Freund, R.: Control mechanisms on \(\#\)-context-free array grammars. In: Păun, Gh. (ed.) Mathematical Aspects of Natural and Formal Languages, pp. 97–137. World Scientific Publishing, Singapore (1994)

    CrossRef  Google Scholar 

  17. Freund, R.: Generalized P-systems. In: Ciobanu, G., Păun, Gh. (eds.) FCT 1999. LNCS, vol. 1684, pp. 281–292. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48321-7_23

    CrossRef  Google Scholar 

  18. Freund, R.: P systems working in the sequential mode on arrays and strings. Int. J. Found. Comput. Sci. 16(4), 663–682 (2005). https://doi.org/10.1142/S0129054105003224

    MathSciNet  CrossRef  MATH  Google Scholar 

  19. Freund, R.: P automata: new ideas and results. In: Bordihn, H., Freund, R., Nagy, B., Vaszil, Gy. (eds.) Eighth Workshop on Non-Classical Models of Automata and Applications, NCMA 2016, Debrecen, Hungary, 29–30 August 2016. Proceedings, books@cg.at, vol. 321, pp. 13–40. ÖsterreichischeComputer Gesellschaft (2016)

    Google Scholar 

  20. Freund, R., Ivanov, S., Staiger, L.: Going beyond turing with P automata: partial adult halting and regular observer \(\omega \)-languages. In: Calude, C.S., Dinneen, M.J. (eds.) UCNC 2015. LNCS, vol. 9252, pp. 169–180. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21819-9_12

    CrossRef  MATH  Google Scholar 

  21. Freund, R., Ivanov, S., Staiger, L.: Going beyond Turing with P automata: regular observer \(\omega \)-languages and partial adult halting. IJUC 12(1), 51–69 (2016)

    MATH  Google Scholar 

  22. Freund, R., Kogler, M., Oswald, M.: A general framework for regulated rewriting based on the applicability of rules. In: Kelemen, J., Kelemenová, A. (eds.) Computation, Cooperation, and Life. LNCS, vol. 6610, pp. 35–53. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-20000-7_5

    CrossRef  Google Scholar 

  23. Freund, R., Leporati, A., Mauri, G., Porreca, A.E., Verlan, S., Zandron, C.: Flattening in (Tissue) P systems. In: Alhazov, A., Cojocaru, S., Gheorghe, M., Rogozhin, Yu., Rozenberg, G., Salomaa, A. (eds.) CMC 2013. LNCS, vol. 8340, pp. 173–188. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54239-8_13

    CrossRef  Google Scholar 

  24. Freund, R., Oswald, M., Staiger, L.: \(\omega \)-P automata with communication rules. In: Martín-Vide, C., Mauri, G., Păun, Gh., Rozenberg, G., Salomaa, A. (eds.) WMC 2003. LNCS, vol. 2933, pp. 203–217. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24619-0_15

  25. Freund, R., Verlan, S.: A formal framework for static (Tissue) P systems. In: Eleftherakis, G., Kefalas, P., Păun, Gh., Rozenberg, G., Salomaa, A. (eds.) WMC 2007. LNCS, vol. 4860, pp. 271–284. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-77312-2_17

  26. Ivanov, S.: Polymorphic P systems with non-cooperative rules and no ingredients. In: Gheorghe, M., Rozenberg, G., Salomaa, A., Sosík, P., Zandron, C. (eds.) CMC 2014. LNCS, vol. 8961, pp. 258–273. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-14370-5_16

    CrossRef  Google Scholar 

  27. Kudlek, M., Martín-Vide, C., Păun, Gh.: Toward a formal macroset theory. In: Calude, C.S., Păun, Gh., Rozenberg, G., Salomaa, A. (eds.) WMC 2000. LNCS, vol. 2235, pp. 123–133. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45523-X_7

    Google Scholar 

  28. van Leeuwen, J., Wiedermann, J.: Computation as an unbounded process. Theor. Comput. Sci. 429, 202–212 (2012). https://doi.org/10.1016/j.tcs.2011.12.040

    MathSciNet  CrossRef  MATH  Google Scholar 

  29. Minsky, M.L.: Computation: Finite and Infinite Machines. Prentice-Hall Inc, Upper Saddle River (1967)

    MATH  Google Scholar 

  30. Păun, Gh.: Computing with membranes. J. Comput. Syst. Sci. 61, 108–143 (1998)

    MathSciNet  CrossRef  Google Scholar 

  31. Păun, Gh., Rozenberg, G., Salomaa, A.: The Oxford Handbook of Membrane Computing. Oxford University Press Inc, New York (2010)

    Google Scholar 

  32. Sosík, P., Valík, O.: On evolutionary lineages of membrane systems. In: Freund, R., Păun, Gh., Rozenberg, G., Salomaa, A. (eds.) WMC 2005. LNCS, vol. 3850, pp. 67–78. Springer, Heidelberg (2006). https://doi.org/10.1007/11603047_5

    CrossRef  Google Scholar 

  33. Bulletin of the International Membrane Computing Society (IMCS). http://membranecomputing.net/IMCSBulletin/index.php

  34. The P Systems Website. http://ppage.psystems.eu/

Download references

Acknowledgements

The authors are very grateful for the useful comments of the referees.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Rudolf Freund .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this paper

Verify currency and authenticity via CrossMark

Cite this paper

Alhazov, A., Freund, R., Ivanov, S. (2018). P Systems with Activation and Blocking of Rules. In: Stepney, S., Verlan, S. (eds) Unconventional Computation and Natural Computation. UCNC 2018. Lecture Notes in Computer Science(), vol 10867. Springer, Cham. https://doi.org/10.1007/978-3-319-92435-9_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-92435-9_1

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-92434-2

  • Online ISBN: 978-3-319-92435-9

  • eBook Packages: Computer ScienceComputer Science (R0)